相关论文: Semi-discrete finite element approximation applied…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
The paper deals with finite element approximations of elliptic Dirichlet boundary control problems posed on two-dimensional polygonal domains. Error estimates are derived for the approximation of the control and the state variables. Special…
This paper presents a conforming finite element semi-discretization of the streamfunction form of the one-layer unsteady quasi-geostrophic equations, which are a commonly used model for large-scale wind-driven ocean circulation. We derive…
We consider residual-based a posteriori error estimators for Galerkin-type discretizations of time-harmonic Maxwell's equations. We focus on configurations where the frequency is high, or close to a resonance frequency, and derive…
A posteriori estimates for mixed finite element discretizations of the Navier-Stokes equations are derived. We show that the task of estimating the error in the evolutionary Navier-Stokes equations can be reduced to the estimation of the…
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain $\Omega \subset \mathbb{R}^{d}$, where $d = 2$ or $3$. The pressure in the model is defined…
We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…
Two important cases, where boundary conditions and solutions of the well-known integrable equations on a semi-strip are uniquely determined by the initial conditions, are rigorously studied in detail. First, the case of rectangular matrix…
The analysis of a delayed generalized Burgers-Huxley equation (a non-linear advection-diffusion-reaction problem) with weakly singular kernels is carried out in this work. Moreover, numerical approximations are performed using the…
This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation.…
This work is concerned with quasi-optimal a-priori finite element error estimates for the obstacle problem in the $L^2$-norm. The discrete approximations are introduced as solutions to a finite element discretization of an accordingly…
We review some results concerning the semi-classical limit for the nonlinear Schrodinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical…
This paper develops and analyzes a semi-discrete and a fully discrete finite element method for a one-dimensional quasilinear parabolic stochastic partial differential equation (SPDE) which describes the stochastic mean curvature flow for…
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
We consider the mathematical analysis and numerical approximation of a system of nonlinear partial differential equations that arises in models that have relevance to steady isochoric flows of colloidal suspensions. The symmetric velocity…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…
In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…
In two recent publications [Kov{\'a}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong convergence of the semi-discrete and fully discrete…